Plane sextics via dessins d'enfants

Alex Degtyarev

Published 2008-12-17, updated 2009-10-01Version 2

We develop a geometric approach to the study of plane sextics with a triple singular point. As an application, we give an explicit geometric description of all irreducible maximal sextics with a type $\bold E_7$ singular point and compute their fundamental groups. All groups found are finite; one of them is nonabelian.